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arXiv:1403.5482 · Europhysics Letters (EPL)

Steady Fock states via atomic reservoir

F. O. Prado, W. Rosado, G. D. de Moraes Neto, M. H. Y. Moussa

Published Jun 26, 2014• 19 citations
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Abstract

In this letter we present a strategy that combines the action of cavity damping mechanisms with that of an engineered atomic reservoir to drive an initial thermal distribution to a Fock equilibrium state. The same technique can be used to slice probability distributions in the Fock space, thus allowing the preparation of a variety of nonclassical equilibrium states.

DOI
10.1209/0295-5075/107/13001

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In this letter we present a strategy that combines the action of cavity damping mechanisms with that of an engineered atomic reservoir to drive an initial thermal distribution to a Fock equilibrium state. The same technique can be used to slice probability distributions in the Fock space, thus allowing the preparation of a variety of nonclassical equilibrium states.
We apply reservoir engineering to construct a thermal environment with controllable temperature in an ultracold atomic Rydberg system. A Boltzmann distribution of the system's eigenstates is produced by optically driving a small environment of ultracold atoms, which is coupled to a photonic continuum through spontaneous emission. This technique provides a useful tool for quantum simulation of both equilibrium dynamics and dynamics coupled to a thermal environment. Additionally, we demonstrate that pure eigenstates, such as Bell states, can be prepared in the Rydberg atomic system using this method.
In this paper we present a protocol to engineer interactions confined to subspaces of the Fock space in trapped ions: we show how to engineer upper-bounded, lower-bounded, and sliced Jaynes-Cummings (JC) and anti-Jaynes-Cummings (AJC) Hamiltonians. The upper-bounded (lower-bounded) interaction acting upon Fock subspaces ranges from $|0\ensuremath{\rangle}$ to $|M\ensuremath{\rangle}$ ($|N\ensuremath{\rangle}$ $\text{to}\phantom{\rule{4pt}{0ex}}\ensuremath{\infty}$), and the sliced one confined to Fock subspace ranges from $|M\ensuremath{\rangle}$ to $|N\ensuremath{\rangle}$, whatever M<NM<NM<N. Whereas the upper-bounded JC or AJC interaction is shown to drive any initial state to a steady Fock state $|N\ensuremath{\rangle}$, the sliced one is shown to produce steady superpositions of Fock states confined to the sliced subspace ${|N\ensuremath{\rangle}\text{,}|N+1\ensuremath{\rangle}}$.
We apply reservoir engineering to construct a thermal environment with controllable temperature in an ultracold atomic Rydberg system. A Boltzmann distribution of the system's eigenstates is produced by optically driving a small environment of ultracold atoms, which is coupled to a photonic continuum through spontaneous emission. This technique provides a useful tool for quantum simulation of dynamics coupled to a thermal environment. Additionally, we demonstrate that pure eigenstates, such as Bell states, can be prepared in the Rydberg atomic system using this method.
We propose an engineered reservoir inducing the relaxation of a cavity field towards nonclassical states. It is made up of two-level atoms crossing the cavity one at a time. Each atom-cavity interaction is first dispersive, then resonant, then dispersive again. The reservoir pointer states are those produced by an effective Kerr Hamiltonian acting on a coherent field. We thereby stabilize squeezed states and quantum superpositions of multiple coherent components in a cavity having a finite damping time. This robust decoherence protection method could be implemented in state-of-the-art experiments.
Reservoir engineering enables the robust and unconditional preparation of pure quantum states in noisy environments. We show how a family of nonclassical states of a mechanical oscillator can be stabilized in a cavity that is parametrically coupled to both the mechanical displacement and the displacement squared. The cavity is driven with three tones, on the red sideband, on the cavity resonance, and on the second blue sideband. The states so stabilized are (squeezed and displaced) superpositions of a finite number of phonons. They show the unique feature of encompassing two prototypes of nonclassicality for bosonic systems: by adjusting the strength of the drives, one can in fact move from a single-phonon- to a Schr\"odinger-cat-like state. The scheme is deterministic, supersedes the need for measurement-and-feedback loops, and does not require initialization of the oscillator to the ground state.